A private name (5)
I believe the answer is:
tommy
I believe this is a double definition.
'a private' is the first definition.
(thesaurus)
'name' is the second definition.
(Other definitions for tommy that I've seen before include "Bread" , "Private soldier (slang)" , "Private in the Army - kind of gun" , "British soldier (informal)" , "Doubtful apostle could be so familiar" .)